Let
The curl is
where 
denotes the partial derivative operator with respect to 
. Recall that
and that for any two vectors 
and 
, 
, and 
.
The cross product reduces to
When you compute the partial derivatives, you'll find that all the components reduce to 0 and
which means 
is indeed conservative and we can find 
.
Integrate both sides of
with respect to 
and
Differentiate both sides with respect to 
and
Now
and differentiating with respect to 
gives
for some constant 
. So
Answer:
a) 512 cm^3
b) 469.125 cm^3
Step-by-step explanation:
8*8*8 = 512 cm^3
or
8^3 = 512 cm^3
3.5^3 = 42.875
512 - 42.875 = 469.125 cm^3
You can round the second answer down
Answer:
3,-3) becomes ; (3 + 5 , -3-12) ; (8,-15)
(7,-10) becomes;( 7 + 5, -10-12) ; (12,-22)
(13,-14) becomes (7 + 13, -14-10) ; (20,-24)
Step-by-step explanation:
What we have to do here is to add 5 to the x-axis value and subtract 12 from the y-axis value
(3,-3) becomes ; (3 + 5 , -3-12) ; (8,-15)
(7,-10) becomes;( 7 + 5, -10-12) ; (12,-22)
(13,-14) becomes (7 + 13, -14-10) ; (20,-24)
